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now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt...
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt...
what exactly is the `` iron curtain '' that sir winston churchill described ?
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt...
you could almost view it as united states influence , a united states colony , they had so much influence with batista . and in the case of vietnam , it was a french colony . so you can imagine , in all of these situations the existing rulers were not that popular .
was the pattern similar in case if iraq invasion ?
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt...
and every time , it ended up in either a us defeat or a stalemate . take whatever lessons there are from this , but it is a kind of an interesting pattern that had happened multiple times , pretty much every engagement that we had during the cold war .
how did the cold war come to an end ?
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt...
and every time , it ended up in either a us defeat or a stalemate . take whatever lessons there are from this , but it is a kind of an interesting pattern that had happened multiple times , pretty much every engagement that we had during the cold war .
how did the cold war end ?
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt...
in the case of cuba , you have people like fidel castro . in vietnam you have people like ho chi minh . and then korea is a little bit different , because you did have a communist nationalist independence movement , but kim il-sung was n't necessarily the leader of that movement .
who were kim-il-sung and ho-chi-mihn ?
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt...
in the case of cuba , you have people like fidel castro . in vietnam you have people like ho chi minh . and then korea is a little bit different , because you did have a communist nationalist independence movement , but kim il-sung was n't necessarily the leader of that movement .
trivia question : what was ho chi minh 's real name ?
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt...
and you could also imagine , there were many capitalists in the united states , who for their own selfish reasons , were afraid of capitalism spreading to the united states , because maybe their wealth would be redistributed . but regardless of what the justification , whether it was a more noble wanting people to have...
what did the soviet union really want to do after they fell ?
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt...
they kind of marginalized them , and installed kim il-sung probably because he was more aligned with them , but he was communist . now the reality is , these guys come in under these very egalitarian , equality for all , let 's get retribution for the wrongs that were done to us before , but probably all of them start ...
why did the guys who ran the soviet union let all the places declare independance ?
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt...
some of the vietnamese who really were aligned with the french , probably got extra favors , and so their wealth was n't necessarily due to innovation or competence , but really just where they fit into the political order . maybe some other people did have legitimate wealth . so you imagine , when any of these type of...
what is the objective `` legitimacy '' for someone 's wealth ?
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt...
but this is just the general pattern that happened every time . and every time , it ended up in either a us defeat or a stalemate . take whatever lessons there are from this , but it is a kind of an interesting pattern that had happened multiple times , pretty much every engagement that we had during the cold war .
then what made soviet union fall which ended of the cold war ?
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt...
so you have to take everything with a grain of salt . and even in this video , i 'll talk about , maybe , some patterns , or some themes , that i 've seen , do n't take that as just the truth . think about it for yourself , if it makes sense , it makes sense .
is it true that ww1 ww2 and the cold war were all caused by the assassination of a prince i did n't even learn about in school ?
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt...
so the general pattern across all of these , is that before the us got involved , and before a communist-leaning regime got involved , these were all , in some ways , subjugated populations . in korea , it was subjugated by the japanese . it was a japanese colony .
wait korea was controlled by the japanese ?
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt...
you could imagine it 's a very popular notion to run on , and depending on how true it is . but it 's a very popular notion to run on , to tell people , look , you 've seen all of these people who 've gotten questionable wealth , and maybe , some of these people who got questionable wealth got it by being aligned with ...
are the people of the communist countries better off than if they were living here ?
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt...
but this is just the general pattern that happened every time . and every time , it ended up in either a us defeat or a stalemate . take whatever lessons there are from this , but it is a kind of an interesting pattern that had happened multiple times , pretty much every engagement that we had during the cold war .
why was the us acting as the enemy and what made russia look at them that way ?
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt...
why do n't we do that with this person here and redistribute that wealth to the rest of society ? and if you 're looking for a political ideology that seems to fit with this idea of trying to correct things that maybe looked wrong during the colonial or the subjugated rule , communism seems to fit that . it 's kind of ...
why was america sort of the '' bad guy '' or so it seems ?
now that we 've done a series of videos on america 's interventions during the cold war in korea , and cuba , and vietnam , i thought it would be fun just to think a little bit about whether there are any patterns here . and once again , in all of these history videos , you have to take anything i say -- or really anyt...
and every time , it ended up in either a us defeat or a stalemate . take whatever lessons there are from this , but it is a kind of an interesting pattern that had happened multiple times , pretty much every engagement that we had during the cold war .
why did massive conflict continue to erupt ( wwi , wwii , cold war , decolonization ) ; why did violent conflict keep recurring during the 1900s ?
hi , this is becca from khan academy , and today i 'm going to be talking about temperance . so , what was the temperance movement ? in this video , i 'll talk a little bit about what temperance was , what its causes were , and how it started to develop in the early-1800s . temperance was the idea that americans drank...
hi , this is becca from khan academy , and today i 'm going to be talking about temperance . so , what was the temperance movement ? in this video , i 'll talk a little bit about what temperance was , what its causes were , and how it started to develop in the early-1800s .
was emily dickenson in the temperance movement ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so now let 's plot them . negative 2 , 1/25 . 1 is going to be like there .
why does 5^-2 becomes 1/25 and not -25 like how 5^2 becomes 25 ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so now let 's plot them . negative 2 , 1/25 . 1 is going to be like there .
ca n't 5^-2 become -25 or is it the fact that because 2 is negative that you have to follow the law of indices ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
this will be my y values . let 's start first with something reasonably negative but not too negative . so let 's say we start with x is equal to negative 2 .
can anyone explain to me why a negative power is always a fraction ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this ...
when do exponential functions come in the real world ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
it 's not going to be on the x-axis . 1/25 is obviously greater than 0 . it 's going to be really , really , really , really , close .
why does any number to the 0 power always become a 1 ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this curve going , you see it 's just going on this someti...
how would one write the range of a exponential function ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
now let 's think about when x is equal to 0 . then y is going to be equal to 5 to the 0-th power , which we know anything to the 0-th power is going to be equal to 1 . so this is going to be equal to 1 .
why is anything to the zero-th power equal to 1 ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so i have positive values over here . so let me draw it like this . so this could be my x-axis .
can you take the derivatives of functions like that ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so that 's y . this is x . that 's a negative 2 .
when the exponential function follows the equation : a ( b ) ^x , what do the a and b stand for ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
and now we can plot it to see how this actually looks . so let me get some graph paper going here . my x 's go as low as negative 2 , as high as positive 2 .
what part of an equation tells you how steep the graph will be ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
now let 's try another value . what happens when x is equal to negative 1 ? then y is 5 to the negative 1 power , which is the same thing as 1 over 5 to the first power , or just 1/5 .
what happens when i 'm graphing a negative number ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so let 's make that my y-axis . and my x values , this could be negative 2 . actually , make my y-axis keep going .
in the positive function , both x and y values increase i presume , and in the negative the x value increases , while the y value decreases ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so now let 's plot them . negative 2 , 1/25 . 1 is going to be like there .
how do you find the asymptote of an exponential function , for example , of y=- ( 2^x ) +1 ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
actually , let me make the scale on the y-axis . so let 's make this . so we 're going to go all the way to 25 .
how do you make an exponential function ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so let 's make that my y-axis . and my x values , this could be negative 2 . actually , make my y-axis keep going .
is there a formula , like y=mx+b or y=a ( x-h ) ^2+k ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
2 comma 25 puts us right about there . and so i think you see what happens with this function , with this graph . the further in the negative direction we go , 5 to ever-increasing negative powers gets closer and closer to 0 , but never quite .
how would you draw a cubic graph when given a function ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
then y is 5 to the negative 1 power , which is the same thing as 1 over 5 to the first power , or just 1/5 . now let 's think about when x is equal to 0 . then y is going to be equal to 5 to the 0-th power , which we know anything to the 0-th power is going to be equal to 1 .
so when x = 0 , y= always no matter what one ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
2 comma 25 puts us right about there . and so i think you see what happens with this function , with this graph . the further in the negative direction we go , 5 to ever-increasing negative powers gets closer and closer to 0 , but never quite .
how do you find the exponential function when the graph is given ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
now let 's try another value . what happens when x is equal to negative 1 ? then y is 5 to the negative 1 power , which is the same thing as 1 over 5 to the first power , or just 1/5 .
in y=ab^x , why will b never be a negative number ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
then y is 5 to the first power , which is just equal to 5 . and let 's do one last value over here . let 's see what happens when x is equal to 2 .
also , when exponential functions are graphed , how does one describe the shift/reflection/dilation ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so this is going to be 5 , 10 , 15 , 20 . and then 25 would be right where i wrote the y , give or take . so now let 's plot them .
what would be the domain and range of the problem sal is using ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
my x 's go as low as negative 2 , as high as positive 2 . and then my y 's go all the way from 1/25 all the way to 25 . so i have positive values over here .
is the a way to determine an exponential function given a table ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so that 's y . this is x . that 's a negative 2 .
why do you have to find the x value ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
i 'm slightly above 0 . i 'm increasing above that , increasing above that . and once i get into the positive x 's , then i start really , really shooting up .
what happens if your zero is 100 and is increasing by 10 % , what would you do then ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way .
will there be a time when the line on the parabola will be straight ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this ...
do all exponential functions have horizontal asymptotes ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
2 comma 25 puts us right about there . and so i think you see what happens with this function , with this graph . the further in the negative direction we go , 5 to ever-increasing negative powers gets closer and closer to 0 , but never quite .
how do you write an exponential function whose graph passes through the given points ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
right at the y-axis , we have y equal 1 . right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase .
why i can not select exponential trend line excel where the number of my data equal zero ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so that 's y . this is x . that 's a negative 2 .
how do you graph an exponential function when x is a decimal ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
now let 's do this point here in orange , negative 1 , 1/5 . negative 1/5 -- 1/5 on this scale is still pretty close . it 's pretty close .
if you are given an exponential graph for instance how can you figure out the equation ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
2 comma 25 puts us right about there . and so i think you see what happens with this function , with this graph . the further in the negative direction we go , 5 to ever-increasing negative powers gets closer and closer to 0 , but never quite .
i know how to graph just a parent function but how would you graph a problem when it also has a number in front and the x on the parent function is subtracting a number ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
my x 's go as low as negative 2 , as high as positive 2 . and then my y 's go all the way from 1/25 all the way to 25 . so i have positive values over here .
is it possible to have the line curve all the way over and into a circle if the numbers get big enough ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this ...
are exponential functions just a function when the variable is the exponent ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way .
how to sum , product , divide or subtract two graphs ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 .
how would you find end behavior , domain and range , positive and negative , and increasing and decreasing points ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so then if i just keep this curve going , you see it 's just going on this sometimes called a hockey stick . it just keeps on going up like this at a super fast rate , ever-increasing rate . so you could keep going forever to the left , and you 'd get closer and closer and closer to 0 without quite getting to 0 .
what is the rate of change ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so that is negative 2 , 1/25 . it 's not going to be on the x-axis . 1/25 is obviously greater than 0 .
the line keeps going on forever in the x direction ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
and now we can plot it to see how this actually looks . so let me get some graph paper going here . my x 's go as low as negative 2 , as high as positive 2 .
how would we graph a fraction ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this ...
how do you find the domain and range of exponential growth and decay functions ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way .
how do you graph something like 5^x+3 ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so this is going to be 5 , 10 , 15 , 20 . and then 25 would be right where i wrote the y , give or take . so now let 's plot them .
what would the horizontal and vertical asymptotes be ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way .
also the domain and range ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this ...
asymptote for an exponential function ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so that 's y . this is x . that 's a negative 2 .
so you substitute the x value into the exponent ex 3^x ( if x is -8 you just plug it in and solve right ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
and i 'll try to center them around 0 . so this will be my x values . this will be my y values .
this is good information , but is there a way to predict the shape of the graph based on the equation 's characteristics , and without tediously plugging in values for x ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this ...
can an exponential growth be used to predict the amount of bacteria cells after a period of time ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so that 's y . this is x . that 's a negative 2 .
is there any relation between log function and e^x ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so now let 's plot them . negative 2 , 1/25 . 1 is going to be like there .
for example if x=2 and y=25 would the inverse of that happen if the number is negative ( x= -2 and y= 1/5 ) ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
and now we can plot it to see how this actually looks . so let me get some graph paper going here . my x 's go as low as negative 2 , as high as positive 2 .
how can i get the roots of a quadratic function ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so let 's make that my y-axis . and my x values , this could be negative 2 . actually , make my y-axis keep going .
does the same method apply for more complicated functions like y = 1000 x 2^-0.04t ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
now let 's do this point here in orange , negative 1 , 1/5 . negative 1/5 -- 1/5 on this scale is still pretty close . it 's pretty close .
does the constant , `` 5 '' , before the exponent represent the steepness or flatness of the exponential function ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so that 's y . this is x . that 's a negative 2 .
why is x always on the left and y always on the right ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
and now we can plot it to see how this actually looks . so let me get some graph paper going here . my x 's go as low as negative 2 , as high as positive 2 .
so how can you tell if a graph is growing or decaying ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so that 's y . this is x . that 's a negative 2 .
how do you graph functions of e^x ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so that 's y . this is x . that 's a negative 2 .
for exponential functions , does sal have anything with a parent function like y=3^ ( x ) and another problem like y=3^ ( x-1 ) where you have to find the domain and range of each and the horizontal asymptote and the y intercept and if its increasing or decreasing ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
1/25 is obviously greater than 0 . it 's going to be really , really , really , really , close . now let 's do this point here in orange , negative 1 , 1/5 .
does the rapidly increasing function ever become vertical or really close to vertical ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
this will be my y values . let 's start first with something reasonably negative but not too negative . so let 's say we start with x is equal to negative 2 .
why ca n't b be negative in exponential functions ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this ...
how to state domain and range of an exponential function ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
that 's negative 1 . that 's 0 . that is 1 .
is there an exponential curve that contains the given point ( 0,2 ) ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
and let 's do one last value over here . let 's see what happens when x is equal to 2 . then y is 5 squared , 5 to the second power , which is just equal to 25 .
what happens when its a problem like -2 ( 3 ) ^x ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
right at x is equal to 0 , we have y is equal to 1 . and then once x starts increasing beyond 0 , then we start seeing what the exponential is good at , which is just this very rapid increase . some people would call it an exponential increase , which is obviously the case right over here . so then if i just keep this ...
can the speed of the expanding universe be graphed as an exponential function ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
this will be my y values . let 's start first with something reasonably negative but not too negative . so let 's say we start with x is equal to negative 2 .
what would the graph of an exponential function with a negative base look like ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so now let 's plot them . negative 2 , 1/25 . 1 is going to be like there .
i 'm curious as to what would happen to the point ( 0,1 ) of an exponential eqn : y=2^x when you are given the equation y=-1/4*2^ ( x-4 ) +5 what is the order of executing these steps ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
2 comma 25 puts us right about there . and so i think you see what happens with this function , with this graph . the further in the negative direction we go , 5 to ever-increasing negative powers gets closer and closer to 0 , but never quite .
how do you find the equation of an exponential function from the graph ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so that 's y . this is x . that 's a negative 2 .
for example , if i have 9^x=16 , how can i find the value of `` x '' ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so now let 's plot them . negative 2 , 1/25 . 1 is going to be like there .
would i plug in let 's say x=0 and solve by saying 4^0-2 -1 4^-3 0 - 2 = - 2 - 1 = -3 f ( x ) =1/64 ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so let me draw it like this . so this could be my x-axis . that could be my x-axis . and then let 's make this my y-axis .
so in this exponential function , the only way the graph will intersect the x-axis or go below it is if the base itself is negative and the domain is an odd integer , correct ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
that 's 0 . that is 1 . and that is positive 2 .
is there any exponential function that does n't intercept the y axis in y = 1 ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
and then finally , we have -- well , actually , let 's try a couple of more points here . let me extend this table a little bit further . let 's try out x is equal to 1 .
however , the area of rain forest is decreasing 20 % each year , and the area of farmland is increasing 20 % each year , complete the table and graph to show the area of each for the next year '' how do you form a table ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
this will be my y values . let 's start first with something reasonably negative but not too negative . so let 's say we start with x is equal to negative 2 .
are exponential functions with negative bases explained or used ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
so that 's y . this is x . that 's a negative 2 .
instead of y = b ^ x can we calculate and plot y = ( -b ) ^ x ?
we 're asked to graph y is equal to 5 to the x-th power . and we 'll just do this the most basic way . we 'll just try out some values for x and see what we get for y . and then we 'll plot those coordinates . so let 's try some negative and some positive values . and i 'll try to center them around 0 . so this will be...
2 comma 25 puts us right about there . and so i think you see what happens with this function , with this graph . the further in the negative direction we go , 5 to ever-increasing negative powers gets closer and closer to 0 , but never quite .
how can we determine if a function is a growth or decay ?
so ever since i first learned about myosin and actin , there was always this thought that popped in my head , a kind of an analogy , if you will . and for a long time , i thought this analogy was pretty much spot-on . but then , i gave it some more thought . and i realized that i was wrong . and so i 'm going to share ...
and c will be -- i 'll draw it right here at the edge . also , almost no force . and you remember , that this actually falls on a curve that we drew out before .
there would not have been a gradual linear reduction in force after a peak ( as was drawn ) , but rather a long linear increase in force with an abrupt drop to zero once the elastic band had snapped , right ?
so ever since i first learned about myosin and actin , there was always this thought that popped in my head , a kind of an analogy , if you will . and for a long time , i thought this analogy was pretty much spot-on . but then , i gave it some more thought . and i realized that i was wrong . and so i 'm going to share ...
and that simply means that we did n't have to add any energy . but specifically , the kind of energy we 're talking about is chemical energy . so when people say there 's a passive process , usually in biology , what we 're talking about is not having to use chemical energy . and , of course , in the slingshot example ...
near the end of the video , rishi talks about the `` things '' being active or passive , and he explains that passive does n't involve chemical energy , but then is active just the opposite ( involves chemical energy ) ?
so ever since i first learned about myosin and actin , there was always this thought that popped in my head , a kind of an analogy , if you will . and for a long time , i thought this analogy was pretty much spot-on . but then , i gave it some more thought . and i realized that i was wrong . and so i 'm going to share ...
and then , i can also , on the x-axis i can put something like , how much i stretched my rubber band . i 'll just put , let 's say , stretch . and then you 'll know that means how much i stretched out the rubber band on my slingshot .
is the sling shot afterall a passive process as it can not stretch on its own ( how about the atp used by our skeletal muscles for the stretch ) ?
so ever since i first learned about myosin and actin , there was always this thought that popped in my head , a kind of an analogy , if you will . and for a long time , i thought this analogy was pretty much spot-on . but then , i gave it some more thought . and i realized that i was wrong . and so i 'm going to share ...
right ? so you 're converting it all to kinetic energy energy of movement . and when you let go of that stone , it happens automatically .
as in it is chemical energy converted to kinetic energy ?
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent...
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing .
what is screening/shielding effect and how does it effect the atomic radius ?
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent...
that 's the nucleus of the other . and they 're sharing electrons . so their electron clouds actually , their electron clouds actually overlap with each other , actually overlap with each other so the covalent bond , there the electrons in that bond could spend some of their time on this atom and some of their time on ...
of electrons and protons , how will the nucleus pull the electrons more closer ?
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent...
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing .
what is the difference between radiation and radioactivity ?
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent...
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing .
( pm is picometer ) what is correct ?
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent...
that 's the nucleus of the other . and they 're sharing electrons . so their electron clouds actually , their electron clouds actually overlap with each other , actually overlap with each other so the covalent bond , there the electrons in that bond could spend some of their time on this atom and some of their time on ...
how many electrons are filled out in each subshell ?
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent...
that 's the reason why the smallest atom of all , the element with the smallest atom is not hydrogen , it 's helium . helium is actually smaller than hydrogen , depending on how you , depending on what technique you use to measure it . that 's because , if we take the simplest case , hydrogen , you have 1 proton in the...
why is helium smaller than hydrogen ?
: let 's think a little bit about the notion of atomic size or atomic radius in this video . at first thought , you might think well this might be a fairly straight-forward thing . if i 'm trying to calculate the radius of some type of circular object i 'm just thinking about well what 's the distance between the cent...
that 's the nucleus of the other . and they 're sharing electrons . so their electron clouds actually , their electron clouds actually overlap with each other , actually overlap with each other so the covalent bond , there the electrons in that bond could spend some of their time on this atom and some of their time on ...
why does n't the electrons around the protons push away the outermost electrons ?